For a matter dominated universe with cosmological constant ,

where G is the gravitational constant, is the density,c is the speed of light,and a is expansion parameter. Therefore,

where H is the Hubble constant and is the density parameter, and the curvature is then

<div ALIGN="CENTER"> <TABLE CELLPADDING=3 BORDER="1"> <TR><TD ALIGN="LEFT">curvature</TD> <TD ALIGN="LEFT">density</TD> <TD ALIGN="LEFT">boundedness</TD> <TD ALIGN="LEFT">closure</TD> </TR> <TR><TD ALIGN="LEFT"><IMG WIDTH="42" HEIGHT="28" ALIGN="MIDDLE" BORDER="0" SRC="http://scienceworld.wolfram.com/physics/cimg1274.gif"></TD> <TD ALIGN="LEFT"><IMG WIDTH="45" HEIGHT="29" ALIGN="MIDDLE" BORDER="0" SRC="http://scienceworld.wolfram.com/physics/cimg1275.gif"></TD> <TD ALIGN="LEFT">bound</TD> <TD ALIGN="LEFT">closed</TD> </TR> <TR><TD ALIGN="LEFT"><IMG WIDTH="42" HEIGHT="14" ALIGN="BOTTOM" BORDER="0" SRC="http://scienceworld.wolfram.com/physics/cimg1276.gif"></TD> <TD ALIGN="LEFT"><IMG WIDTH="45" HEIGHT="14" ALIGN="BOTTOM" BORDER="0" SRC="http://scienceworld.wolfram.com/physics/cimg1207.gif"></TD> <TD ALIGN="LEFT">marginally bound</TD> <TD ALIGN="LEFT">flat</TD> </TR> <TR><TD ALIGN="LEFT"><IMG WIDTH="42" HEIGHT="28" ALIGN="MIDDLE" BORDER="0" SRC="http://scienceworld.wolfram.com/physics/cimg1277.gif"></TD> <TD ALIGN="LEFT"><IMG WIDTH="45" HEIGHT="29" ALIGN="MIDDLE" BORDER="0" SRC="http://scienceworld.wolfram.com/physics/cimg1278.gif"></TD> <TD ALIGN="LEFT">unbound</TD> <TD ALIGN="LEFT">open</TD> </TR> </TABLE> </DIV>
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